Norm of a Bloch-Type Projection

Abstract

In this paper, we obtain the exact norm of the following integral operator $P^{\alpha }_{t}$

$$\begin{aligned} P^{\alpha }_{t}f(z)=\int _{\mathbb {B}_{n}}\frac{f(w)}{(1- \langle z,w \rangle )^{n+t+\alpha }}dv_{t}(w),\ \alpha>0,\ t>-1, \end{aligned}$$

from $L^{\infty }(\mathbb {B}_{n})$ onto Bloch-type spaces $\mathcal {B}_\alpha$ over the unit ball $\mathbb {B}_{n}$, which can be regarded as an another extension of the classical Bergman projection.